Aims. We set out to study the atmosphere of WASP-80b, a warm inflated gas giant with an equilibrium temperature of ~800 K, using ground-based transmission spectroscopy covering the spectral range from 520 to 910 nm. The observations allow us to probe the existence and abundance of K and Na in WASP-80b’s atmosphere, existence of high-altitude clouds, and Rayleigh-scattering in the blue end of the spectrum. Methods. We observed two spectroscopic time series of WASP-80b transits with the OSIRIS spectrograph installed in the Gran Telescopio Canarias (GTC), and use the observations to estimate the planet’s transmission spectrum between 520 nm and 910 nm in 20 nm-wide passbands, and around the K I and Na I resonance doublets in 6 nm-wide passbands. We jointly model three previously published broadband datasets consisting of 27 light curves, prior to a transmission spectroscopy analysis in order to obtain improved estimates of the planet’s orbital parameters, average radius ratio, and stellar density. The parameter posteriors from the broadband analysis are used to set informative priors on the transmission spectroscopy analysis. The final transmission spectroscopy analyses are carried out jointly for the two nights using a divide-by-white approach to remove the common-mode systematics, and Gaussian processes to model the residual wavelength-dependent systematics. Results. We recover a flat transmission spectrum with no evidence of Rayleigh scattering or K I or Na I absorption, and obtain an improved system characterisation as a by-product of the broadband- and GTC-dataset modelling. The transmission spectra estimated separately from the two observing runs are consistent with each other, as are the transmission spectra estimated using either a parametric or nonparametric systematics model. The flat transmission spectrum favours an atmosphere model with high-altitude clouds over cloud-free models with stellar or sub-stellar metallicities. Conclusions. Our results disagree with the recently published discovery of strong K I absorption in WASP-80b’s atmosphere based on ground-based transmission spectroscopy with FORS2 at VLT.